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Adyquin
In my opinion, the angle facing the longest side is always the greatest angle. In this case angle B is facing 6 which is the longest side. Therefore B is greater.
Answer B.

That logic is generally correct, but you're missing the fact that both B and D point to two side lengths since they are bisected by the diagonal.
B splits 6 and 4, and D splits 5 and 3. So it isn't simply that 6 is the biggest number, but rather the combination of the two angles is greater.
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Bunuel

In the figure, which one of the following angles is the greatest?


(A) ∠A
(B) ∠B
(C) ∠C
(D) ∠D
(E) ∠CDB

Source: Nova GMAT
Difficulty Level: 550
Attachment:
figure.jpg

In a triangle, angle opposite to the largest side is the greatest.

So in triangle ABD, angle B is greater than angle A and angle D. (By angle B here, I mean angle ABD. By angle D here, I mean angle ADB)
In triangle BDC, angle B is greater than angle D and angle C. (Same as above)

Hence the combined angle B will be greater than angle A, combined angle D and angle C.

Answer (B)
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